# zbMATH — the first resource for mathematics

Modeling crack propagation in polycrystalline microstructure using variational multiscale method. (English) Zbl 1400.74096
Summary: Crack propagation in a polycrystalline microstructure is analyzed using a novel multiscale model. The model includes an explicit microstructural representation at critical regions (stress concentrators such as notches and cracks) and a reduced order model that statistically captures the microstructure at regions far away from stress concentrations. Crack propagation is modeled in these critical regions using the variational multiscale method. In this approach, a discontinuous displacement field is added to elements that exceed the critical values of normal or tangential tractions during loading. Compared to traditional cohesive zone modeling approaches, the method does not require the use of any special interface elements in the microstructure and thus can model arbitrary crack paths. The capability of the method in predicting both intergranular and transgranular failure modes in an elastoplastic polycrystal is demonstrated under tensile and three-point bending loads.

##### MSC:
 74R10 Brittle fracture 74M25 Micromechanics of solids 74S05 Finite element methods applied to problems in solid mechanics
Full Text:
##### References:
 [1] Allison, J.; Backman, D.; Christodoulou, L., Integrated computational materials engineering: a new paradigm for the global materials profession, Journal of the Minerals, Metals, and Materials Society, 58, 11, 25-27, (2006) [2] Harren, S. V.; Asaro, R. J., Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model, Journal of the Mechanics and Physics of Solids, 37, 2, 191-232, (1989) · Zbl 0669.73040 [3] Bronkhorst, C. A.; Kalidindi, S. R.; Anand, L., Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 341, 1662, 443-477, (1992) [4] Sundararaghavan, V.; Zabaras, N., Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization, International Journal of Plasticity, 22, 10, 1799-1824, (2006) · Zbl 1136.74315 [5] Auriault, J. L.; Boutin, C.; Geindreau, C., Homogenization of Coupled Phenomena in Heterogenous Media. Homogenization of Coupled Phenomena in Heterogenous Media, Iste Series, (2009), New York, NY, USA: John Wiley & Sons, New York, NY, USA [6] Miller, R.; Ortiz, M.; Phillips, R.; Shenoy, V.; Tadmor, E. B., Quasicontinuum models of fracture and plasticity, Engineering Fracture Mechanics, 61, 3-4, 427-444, (1998) [7] Dunne, F.; Wilkinson, A.; Allen, R., Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal, International Journal of Plasticity, 23, 2, 273-295, (2007) · Zbl 1127.74315 [8] Kumar, A.; Dawson, P. R., The simulation of texture evolution with finite elements over orientation space I. Development, Computer Methods in Applied Mechanics and Engineering, 130, 3-4, 227-246, (1996) · Zbl 0861.73073 [9] Sundararaghavan, V.; Zabaras, N., On the synergy between texture classification and deformation process sequence selection for the control of texture-dependent properties, Acta Materialia, 53, 4, 1015-1027, (2005) [10] Sun, S.; Sundararaghavan, V., A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry, Acta Materialia, 60, 13-14, 5233-5244, (2012) [11] Camacho, G. T.; Ortiz, M., Adaptive Lagrangian modelling of ballistic penetration of metallic targets, Computer Methods in Applied Mechanics and Engineering, 142, 3-4, 269-301, (1997) · Zbl 0892.73056 [12] Ortiz, M.; Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, 44, 9, 1267-1282, (1999) · Zbl 0932.74067 [13] Spearot, D. E.; Jacob, K. I.; McDowell, D. L., Non-local separation constitutive laws for interfaces and their relation to nanoscale simulations, Mechanics of Materials, 36, 9, 825-847, (2004) [14] Yamakov, V.; Saether, E.; Phillips, D. R.; Glaessgen, E. H., Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum, Journal of the Mechanics and Physics of Solids, 54, 9, 1899-1928, (2006) · Zbl 1120.74782 [15] Lee, S.; Sundararaghavan, V., Calibration of nanocrystal grain boundary model based on polycrystal plasticity using molecular dynamics simulations, International Journal for Multiscale Computational Engineering, 8, 5, 509-522, (2010) [16] Zavattieri, P. D.; Espinosa, H. D., Grain level analysis of crack initiation and propagation in brittle materials, Acta Materialia, 49, 20, 4291-4311, (2001) [17] Wei, Y. J.; Anand, L., Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals, Journal of the Mechanics and Physics of Solids, 52, 11, 2587-2616, (2004) · Zbl 1084.74014 [18] Iesulauro, E., Decohesion of grain boundaries in three-dimensional statistical representations of aluminum polycrystals [19] Rudraraju, S. S.; Salvi, A.; Garikipati, K.; Waas, A. M., In-plane fracture of laminated fiber reinforced composites with varying fracture resistance: experimental observations and numerical crack propagation simulations, International Journal of Solids and Structures, 47, 7-8, 901-911, (2010) · Zbl 1193.74144 [20] Garikipati, K.; Hughes, T. J., A study of strain localization in a multiple scale framework the one-dimensional problem, Computer Methods in Applied Mechanics and Engineering, 159, 3-4, 193-222, (1998) · Zbl 0961.74009 [21] Garikipati, K., A variational multiscale method to embed micromechanical surface laws in the macromechanical continuum formulation, Computer Modeling in Engineering & Sciences, 3, 2, 175-184, (2002) · Zbl 1098.74007 [22] Moës, N.; Belytschko, T., Extended finite element method for cohesive crack growth, Engineering Fracture Mechanics, 69, 7, 813-833, (2002) [23] Song, J.-H.; Belytschko, T., Cracking node method for dynamic fracture with finite elements, International Journal for Numerical Methods in Engineering, 77, 3, 360-385, (2009) · Zbl 1155.74415 [24] Sukumar, N.; Srolovitz, D. J.; Baker, T. J.; Prévost, J.-H., Brittle fracture in polycrystalline microstructures with the extended finite element method, International Journal for Numerical Methods in Engineering, 56, 14, 2015-2037, (2003) · Zbl 1038.74652 [25] Rudraraju, S., On the Theory and Numerical Simulation of Cohesive Crack Propagation with Application to Fiber-Reinforced Composites, (2011), Ann Arbor, Mich, USA: University of Michigan, Ann Arbor, Mich, USA [26] Rudraraju, S.; Salvi, A.; Garikipati, K.; Waas, A. M., Predictions of crack propagation using a variational multiscale approach and its application to fracture in laminated fiber reinforced composites, Composite Structures, 94, 11, 3336-3346, (2012) [27] Anand, L.; Kothari, M., A computational procedure for rate-independent crystal plasticity, Journal of the Mechanics and Physics of Solids, 44, 4, 525-558, (1996) · Zbl 1054.74549 [28] Kumar, A.; Dawson, P. R., The simulation of texture evolution with finite elements over orientation space II. Application to planar crystals, Computer Methods in Applied Mechanics and Engineering, 130, 3-4, 247-261, (1996) · Zbl 0861.73073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.